1=-5t^2+15t-1

Solution for 1=-5t^2+15t-1 equation:

1=-5t^2+15t-1

We move all terms to the left:

1-(-5t^2+15t-1)=0

We get rid of parentheses

5t^2-15t+1+1=0

We add all the numbers together, and all the variables

5t^2-15t+2=0

a = 5; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·5·2
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{185}}{2*5}=\frac{15-\sqrt{185}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{185}}{2*5}=\frac{15+\sqrt{185}}{10}
$